Applying Remainders

Using Number Properties

Problem: “Michael builds a string of beads using 3 colours, starting at white, black, then red then repeating the pattern.

He continues building using 103 beads altogether. What colour is the last bead?” 
(Possible answer: 103 ÷ 3 = 34 remainder 1. So there are 34 groups of 3 and the last one is white.)

Discuss what colour the last one will be if the remainder is 1, 2, or 0.
Examples: Find the colour of the last bead if there are these numbers of beads: 56 123     678           828           8 987

Understanding Number Properties:

Make up a bead problem like Michael’s where the number of beads is over 10 000.

Problem: “Michael builds a pattern of counters with four colours A, B, C, and D. So the counters look like ABCD ABCD ABCD ABCD .... What colour is the 45 679th bead?”

(Possible answer: By calculator: 45 679 ÷ 4 =11419.75. The last bead will be C.)

Example: Find the colour of the last bead if there are these numbers of beads: 5 489 12 788             823 451                 34 500               28 987

Problem: “Starting at 12 o’clock, Michael records the hour hand of a 12-hour clock going around for 12 345 hours. What time does the clock show at the end of the 12 345 hours?”